
TL;DR
The paper introduces a symplectic elimination algorithm that reduces symplectic matrices to diagonal form and provides a new matrix decomposition similar to SR and QR decompositions.
Contribution
It develops a novel symplectic elimination algorithm and a related matrix decomposition, expanding the tools for symplectic matrix analysis.
Findings
Algorithm effectively reduces symplectic matrices to diagonal form
Provides a new matrix decomposition similar to SR and QR
Enables new approaches in symplectic matrix analysis
Abstract
We develop the symplectic elimnation algorithm. This algorithm using simple row operations reduce a symplectic matrix to a diagonal matrix. This algorithm gives rise to a decomposition of an arbitrary matrix into a product of a symplectic matrix and a reduced matrix. This decomposition is similar to the SR decomposition studied for a long time, which is analogous to the QR decomposition.
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Taxonomy
TopicsMatrix Theory and Algorithms · Polynomial and algebraic computation · Quantum Computing Algorithms and Architecture
